Constraints on the bulk Lorentz factor of gamma-ray burst jets from Fermi/LAT upper limits

It is largely recognized that gamma-ray burst (GRB) jets involve ultrarelativistic motion. However, the value of the Lorentz factor Γ₀ is still not clear and only lower limits are known for most bursts. We suggest here a new method to obtain upper limits on Γ₀. The early highenergy synchrotron afterglow flux depends strongly on Γ₀. Upper limits on GeV emission therefore provide upper limits on Γ₀. Applying this method to 190 Fermi GRBs which have not been detected by the Fermi-LAT, we place upper limits on the high-energy afterglow flux, and in turn on Γ₀. For bursts at a typical redshift z = 2, we find values of the order of 200 (and above) for a homogeneous density medium, and in the range 100-400 for a wind-like medium. These upper limits are consistent with (and are very close to) lower limits and direct estimates inferred using other methods, suggesting that the typical Lorentz factors of GRB jets are of the order of a few hundred.